Mathematics, 05.06.2020 01:03, leannamat2106

The sample space, S, of a coin being tossed three times is shown below, where H and T denote the coin landing on heads and tails respectively.

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The probability distribution for the number of heads occurring in three coin tosses are P(X1) = 1, P(X2)= 2/3, P(X3)= 2/3, P(X4)= 1/3, P(X5)= 2/3, P(X6)= 1/3, P(X7)= 1/3 and P(X8)= 0

Step-by-step explanation:

The question is incomplete. Here is the complete question;

The sample space, S, of a coin being tossed three times is shown below, where Hand T denote the coin

landing on heads and tails respectively.

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Let X = the number of times the coin comes up heads. What is the probability distribution for the number of heads occurring in three coin tosses?

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome/total outcome of event

From the question given, the total number of sample space will be our total outcome during each toss = 3

If X is the number of times the coin comes up heads, the number of times the coin turn up all heads will be the expected outcome during each throw.

Probability distribution P(Xi)= $\frac{n(Xi)}{n(S)}$

Xi is the probability that the head turns up at each throw.

n(Xi) is the expected outcome during each toss

n(S) is the total outcome during each toss

During the first throw, the head turns up three times (HHH), the probability that heads turns up ia 3/3 = 1

P(X1) = 1

During the second, third and fifth throw, the head turns up two times, the probability that heads turns up during this times will be 2/3

P(X2)= 2/3

P(X3)= 2/3

P(X5)= 2/3

During the fourth, sixth and seventh throw, the head turns up just once, the probability that heads turns up during this times will be 1/3

P(X4)= 1/3

P(X6)= 1/3

P(X7)= 1/3

Since no head turns up during the eight throw, the probability that heads turns up during this time will be 0/3 which is 0.

P(X8)= 0

The probability distribution for the number of heads occurring in three coin tosses are P(X1) = 1, P(X2)= 2/3, P(X3)= 2/3, P(X4)= 1/3, P(X5)= 2/3, P(X6)= 1/3, P(X7)= 1/3 and P(X8)= 0