Anu, Priya and Jyoti were fighting to get the first chance in a game. Anu says, "Let us toss two coins. If both heads appear, Priya will take first chance, if both tails appear Jyoti will get it and if one head and one tail appears, I will get the chance”. What is the probability of Anu, Priya and Jyoti getting the first chance?

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12, 14, 14

14, 12, 14

12, 12, 14

14, 12, 12

answer is A.

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Detailed Solution

Given, Anu, Priya and Jyoti were fighting to get first chance in a game. Anu says, "let us toss two coins. If both heads appear, Priya will take first chance, if both tails appear Jyoti will get it and if one head and one tail appears, I will get the chance”.
The probability of an event occurring is calculated by dividing the number of favourable outcomes by the total number of outcomes; that is,

Probability of an event = Number of favourable outcomes Total number of outcomes

Tossing two coins yields the results hh, ht, th, and tt where h stands for head and t for tail.
There are a total of four possible outcomes.
Determine the most favourable outcome so that Anu has a chance.
If one head and one tail appear, Anu gets first chance at ht and th.
Anu has received two favourable outcomes.
Determine the likelihood that Anu gets the first chance by dividing the number of favourable outcomes by the total number of possible outcomes, we get 2 and 4, respectively.

Probability = Number of favourable outcomes Total number of possible outcomes = 24 = 12

Thus, the probability of Anu getting chance is

12

. Determine the most favourable outcome so that Priya has a chance.
If both heads appear, the favourable outcome is that Priya gets first chance.
Priya has received one favourable outcome.
Determine the likelihood that Priya will be given first opportunity by dividing the number of favourable outcomes by the total number of possible outcomes, 1 and 4 are obtained.

Probability = Number of favourable outcomes Total number of possible outcomes = 14

Thus, the probability of Priya getting chance is

14

. Determine the most favourable outcome so that Jyoti has a chance.
If both heads appear, the favourable outcome is tt, which means Jyoti gets first chance. Jyoti has received one favourable outcome.
Determine the likelihood that Jyoti gets the first chance.
Find the probability by dividing the number of favourable outcomes by the total number of possible outcomes, we get 1 and 4, respectively.