Question

What is the probability that you would get heads-up when flipping a coin ONE time?

What is the probability that you would get heads-up when flipping a coin TEN times?

What is the probability that you would get heads-up on two coins flipped at the same time?

What is the probability that you would roll a 5 on a single dice if you rolled it five times?

What is the probability that you would roll a 3 on a single dice if you rolled it five times?

Answer 1

Probability = Favorable Outcomes / Total Outcome
Flipping a coin has 2 outcomes. Either heads or tails.

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(a) Getting heads when flipping one coin = 1 / 2 = 0.5

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(b) Getting heads each time for 10 times = 1 / 2 * 1/ 2 * 1/2 .... 10 times = (1 / 2)¹⁰ = 1 / 1024 = 0.001

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(c) Getting heads on 2 coins = 1 /2 * 1/2 = 1 / 4 = 0.25

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For problems (d) and (e)

Throwing a dice has 6 outcomes. Either 1, 2, 3, 4, 5 or 6.

Probability of getting any one of these = 1/6

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(d) First we need to choose a dice to get a 5, which can be done in 5C1 = 5 ways

P(getting a 5) = 1/6

P(not getting a 5 on the other 4 dice) = 5/6 * 5/6 * 5/6 * 5/6 = 625/1296

Therefore the required probability = 5 * 1/6 * 625/1296 = 3125 / 7776 = 0.4019

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(e) The probability is the same as (d) because the probability of rolling a 3 is the same as rolling any number.

Therefore the required probability = 5 * 1/6 * 625/1296 = 3125 / 7776 = 0.4019

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