Question

A die is tossed 3 times. What is the probability of
(a) No fives turning up? (b) 1 five? (c) 3 fives?

Answer 1

When a die is rolled up the probability of coming three is one upon six

Answer 2

a. The probability of no five turning up is 0.5787

b. The probability of 1 five is 0.34722

c. The probability of 3 fives is 4.6296 × 10⁻³.

Given that,

A dice is tossed 3 times.

We have to find the probability of no five turning up and 1 five and 3 fives.

We know that,

This is a binomial distribution because there are only 2 possible outcomes (we get a 5 or we don't).

Now, n=3 for each part.

Let X= number of fives appearing.

(a) Here, x=0

P(X=0) = $C^n_x p^x q^{n-x}$ = $C^3_0 (\frac{1}{6}) ^0 (\frac{5}{6}) ^{3-0}$ = $\frac{125}{216}$ =0.5787

(b) Here, x=1

P(X=1) = $C^n_x p^x q^{n-x}$ = $C^3_1 (\frac{1}{6}) ^1 (\frac{5}{6}) ^{3-1}$ = $\frac{75}{216}$ = 0.34722

(c) Here, x=3

P(X=3) = $C^n_x p^x q^{n-x}$ = $C^3_3 (\frac{1}{6}) ^3 (\frac{5}{6}) ^{3-3}$ = $\frac{1}{216}$ =4.6296 × 10⁻³

Therefore, The probability of no five turning up is 0.5787 and 1 five is 0.34722 and 3 fives is 4.6296 × 10⁻³.

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