Three different coins are tossed together what is the probability of getting at most two heads

Three different coins are tossed together. Find the probability of getting(i) exactly two heads(ii) at least two heads

(iii) at least two tails.

When three coins are tossed together, the possible outcomes areHHH, HTH, HHT, THH, THT, TTH, HTT, TTTtherefore,Total number of possible outcomes = 8(i) Favourable outcomes of exactly two heads are HTH, HHT, THHTotal number of favourable outcomes= 3Probability of getting exactly two heads = 3/8(ii) Favourable outcomes of at least two heads are HHH, HTH, HHT, THHTotal number of favourable outcomes =4Probability of getting at least two heads =4/8 = 1/2(iii)Favourable outcomes of at least two tails are THT, TTH, HTT, TTTTotal number of favourable outcomes =4

Probability of getting at least two tails - 4/8 = 1/2

Answer

Verified

Hint: First, before proceeding for this, we must know that we require the total number of cases when three different coins are tossed which are 8. Then, we will find the favourable outcomes for all the cases that are asked in the question. Then, after getting that we will get the probabilities of all the cases as required.

Complete step by step answer:

In this question, we are supposed to find the probabilities of different conditions as given in the question when three different coins are tossed together.So, before proceeding for this, we must know that we requires the total number of cases when three different coins are tossed as:(HHH, HHT, THH, HTH, TTH, THT, HTT, TTT)So, we get the total number of cases when three different coins are tossed as 8.Now, for the case (i), we are asked to find the probability when we get exactly two heads.Then, we get the favourable cases as:(HHT, THH, HTH) which are 3 in number.So, we get the probability of exactly two heads in 3 throws of different coins as:$\dfrac{3}{8}$Now, for the case (ii), we are asked to find the probability when we get at least one tail.Then, we get the favourable cases as:(HHT, THH, HTH, TTH, TTT, THT, HTT) which are 7 in number.So, we get the probability of at least one tail in 3 throws of different coins as:$\dfrac{7}{8}$Now, for the case (iii), we are asked to find the probability when we get at most two heads.Then, we get the favourable cases as:(HHT, THH, HTH, TTH, TTT, THT, HTT) which are 7 in number.So, we get the probability of at most two heads in 3 throws of different coins as:$\dfrac{7}{8}$Now, for the case (iv), we are asked to find the probability when we get at most two tails.Then, we get the favourable cases as:(HHT, THH, HTH, HHH, TTH, THT, HTT) which are 7 in number.So, we get the probability of at most two tails in 3 throws of different coins as:$\dfrac{7}{8}$Now, for the case (v), we are asked to find the probability when we get at least two tails.Then, we get the favourable cases as:(HTT, THT, TTH, TTT) which are 4 in number.So, we get the probability of at least two tails in 3 throws of different coins as:$\dfrac{4}{8}$Now, for the case (vi), we are asked to find the probability when we get at most one head.Then, we get the favourable cases as:(HTT, THT, TTH, TTT) which are 4 in number.So, we get the probability of at most one head in 3 throws of different coins as:$\dfrac{4}{8}$Now, for the case (vii), we are asked to find the probability when we get at least one head.Then, we get the favourable cases as:(HHT, THH, HTH, TTH, THT, HTT, TTT) which are 7 in number.So, we get the probability of at least one head in 3 throws of different coins as:$\dfrac{7}{8}$

Hence, we get the all required probabilities.

Note:

Now, to solve these types of questions we need to know some of the basics of probability in advance to proceed in these types of questions. So, probability is defined as the ratio of the favourable outcomes to the total outcomes and it is always in the form of ratio.