Problems top top coin toss probability are defined here with different examples.

You are watching: If a coin is tossed twice the chance of getting at least one head is 100

When us flip a coin there is constantly a probability to gain a head or a tail is 50 percent.Suppose a coin tossed then we obtain two feasible outcomes either a ‘head’ (H) or a ‘tail’ (T), and also it is difficult to predict even if it is the an outcome of a toss will be a ‘head’ or ‘tail’.

The probability for equally most likely outcomes in an occasion is:

Number the favourable outcomes ÷ Total number of possible outcomes


Total number of possible outcomes = 2

(i) If the favourable outcome is head (H).

Number that favourable outcomes = 1.

Therefore, P(getting a head)

variety of favorable outcomes = P(H) = total number of possible outcomes

= 1/2.

(ii) If the favourable outcome is tail (T).

Number of favourable outcomes = 1.

Therefore, P(getting a tail)

number of favorable outcomes = P(T) = total variety of possible outcomes

= 1/2.

Word troubles on Coin Toss Probability:

1. A coin is tossed twice at random. What is the probability of getting

(i) at the very least one head

(ii) the very same face?

Solution:

The feasible outcomes room HH, HT, TH, TT.

So, total variety of outcomes = 4.

(i) variety of favourable outcomes for event E

                              = variety of outcomes having actually at the very least one head

                              = 3 (as HH, HT, TH are having at the very least one head).

So, by definition, P(F) = (frac34).

(ii) number of favourable outcomes for event E

                              = variety of outcomes having actually the same face

                              = 2 (as HH, TT are have actually the very same face).

So, through definition, P(F) = (frac24) = (frac12).

2.

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 If three fair coins space tossed randomly 175 times and it is discovered that three heads appeared 21 times, two heads appeared 56 times, one head appeared 63 times and also zero head showed up 35 times. 

What is the probability the getting 

(i) 3 heads, (ii) two heads, (iii) one head, (iv) 0 head. 

Solution: 

Total variety of trials = 175. 

Number of times three heads showed up = 21. 

Number of times 2 heads appeared = 56. 

Number of time one head showed up = 63. 

Number of times zero head showed up = 35. 

Let E1, E2, E3 and E4 be the events of getting three heads, two heads, one head and also zero head respectively.

(i)P(getting three heads)

number of times 3 heads appeared = P(E1) = total number of trials

= 21/175

= 0.12

(ii) P(getting 2 heads)

variety of times 2 heads appeared = P(E2) = total variety of trials

= 56/175

=0.32

(iii) P(getting one head)

variety of times one head appeared = P(E3) = total variety of trials

=63/175

= 0.36

(iv) P(getting zero head)

number of times zero head showed up = P(E4) = total number of trials

= 35/175

= 0.20

Note: Remember as soon as 3 coinsare tossed randomly, the only feasible outcomes

are E2, E3, E4 andP(E1) + P(E2) + P(E3) + P(E4)

= (0.12 + 0.32 + 0.36 + 0.20)

= 1

3. two coins room tossed randomly 120 times and it is uncovered that 2 tailsappeared 60 times, one tailappeared 48 times and also no tail showed up 12 times.

If 2 coins room tossed in ~ random, what is theprobability of acquiring

(i) 2 tails,

(ii) 1 tail,

(iii) 0 tail

Solution:

Total number oftrials = 120

Number of times 2 tails appear= 60 

Number of times 1 tail appears= 48

Number of times 0 tail appears= 12

Let E1, E2 and E3 be the occasions of acquiring 2 tails, 1 tail and also 0 tail respectively.

(i) P(getting2 tails)

variety of times 2 tails show up = P(E1) = total number of trials

= 60/120

= 0.50

(ii) P(getting 1 tail)

variety of times 1 tail show up = P(E2) = total number of trials

= 48/120

= 0.40

(iii) P(getting0 tail)

variety of times no tail appear = P(E3) = total number of trials

= 12/120

= 0.10

Note:

Remember if tossing 2 coins simultaneously, the only feasible outcomes are E1, E2, E3 and, P(E1) + P(E2) + P(E3)

= (0.50 + 0.40 + 0.10)

= 1


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4. Suppose a fair coin is randomlytossed because that 75 times and it is discovered that head transforms up 45times and also tail 30 times. What is the probability of acquiring (i)a head and also (ii) a tail?

Solution:

Total number of trials = 75.

Number of time head turns up = 45

Number of times tail transforms up = 30

(i) let X it is in the event ofgetting a head.

P(getting a head)

number of times head turns up = P(X) = total number of trials

= 45/75

= 0.60

(ii) allow Y bethe event of getting a tail.

P(getting a tail)

number of times tail turns up = P(Y) = total variety of trials

= 30/75

= 0.40

Note: Remember when afair coin is tossed and then X and Y arethe only feasible outcomes, and