Question

If the probability of winning a carnival game was 2/5 and Max played it five times, write an expression that would calculate the probability he won the first three games and lost the last two

Answer 1

Prob(winning carnival game) = 2/5 
Prob(losing carnival game) = 3/5 

Prob (Max wins first 3 games, but loses last 2 games) 

= Prob(Max wins game 1) * Prob(Max wins game 2) * Prob(Max wins game 3) * Prob(Max loses game 4) * Prob(Max loses game 5) 

Answer 2

The probability of Max winning the first three games while losing the rest two is 0.023.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

As it is given that the probability of winning the game is 2/5. Since the sum of all the probability of an event is 1, therefore, the probability of losing the game can be written as,

Sum of all probability = Probability of winning + Probability of losing

$1 = \dfrac25+\text{(Probability of losing)}\\\\\text{(Probability of losing)}=\dfrac35$

Thus, the probability of losing the game is 3/5.

As we need to calculate the probability of Max winning the first three games while he losing the rest two. Therefore,

$P = \dfrac25 \times \dfrac25 \times \dfrac25 \times \dfrac35 \times \dfrac35 = \dfrac{72}{3125} = 0.023$

Hence, the probability of Max winning the first three games while losing the rest two is 0.023.

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