Question

# on a game show a contestants have a chance to spin a wheel. the wheel is...

on a game show a contestants have a chance to spin a wheel. the wheel is divided into slots, half of the slots say win and half say lose. there is a pointer above the top of the wheel, if the pointer points to a win slot when the wheel stops then the contestant wins cash prize. if the pointer points to a lose slot then the contestant wins nothing. The contestant spins the wheel 3 times. Let x be the number of times they win. What is the probability of winning 2 cash prizes?

If half the slots re to win and half to lose.

P(win) = P(lose) = 1 / 2

= 0.5

Now we assume that each spin is independent of the previous one. So to get the probability of winning and losing we will just multiply them.

If there 3 games and we win 2 games then it means we lose 1 gaeme.

P(winning 2 games and 1 game) = P(win) * P(win) * P(lose)

= 0.5 * 0.5 * 0.5

= 0.125

Now there are 3 ways in which we can win 2 games out of 3.

win win lose

win lose win

lose win win

we can also use combination function 3C2 = (3!) / [(3 - 2)! 2!] = 3

Therefore we also need to multiply the number of options.

P(winning 2 games) = 3 * 0.125

P(winning 2 games) =