An experiment is given together with an event. Find the (modeled) probability of

Question

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the coins are distinguishable and fair, and that what is observed are the faces uppermost. (Compare with Exercises 1-10 in Section 7.1) Four coins are tossed; the result is at most one head. An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost. (Compare with Exercises 1-10 in Section 7.1) Two dice are rolled: the numbers add to 9.

Explanation / Answer

(1) 4 coins tossed. To find the probability of at most 1 head:

P(at most 1 head) = (no head) + P(1 head)

Let X = getting head in one throw.

p = 0.5

q = 0.5

P(X=0) = 0.54 = 0.0625

P(X=1) = 4 0.53 0.5 = 0.25

So, Probability of at most 1 head = P(0) + P(1) = 0.0625 + 0.25 = 0.3125

(2) 2 dices are thrown. To find probability of numbers added to 9:

Total number of events = 6 X 6 = 36

Events favourable to occurrence of event:

(3,6)

(4,5)

((5,4)

(6,3)

So,

Number of events favourable to occurrence of event = 4

So, Probability of the numbers added to 9 = 4/36 = 0.1111

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