The game involves tossing a penny and a dime along with rolling a die. to win the penny land heads up, the dime land tails up and roll a 6 on the die. what is the probability that he will win on the first play
1/2 * 1/2 * 1/6
To find the probability of winning on the first play, we need to determine the probabilities of each event happening individually and then multiply them together.
1. The probability of the penny landing heads up: A fair penny has two sides (heads and tails), so the probability of it landing heads up is 1/2.
2. The probability of the dime landing tails up: Similar to the penny, the probability of the dime landing tails up is also 1/2.
3. The probability of rolling a 6 on a fair die: A fair die has six sides (numbered from 1 to 6), so the probability of rolling a 6 is 1/6.
To calculate the probability of all three events happening together, we multiply the probabilities:
Probability = (1/2) * (1/2) * (1/6) = 1/24
Therefore, the probability of winning on the first play is 1/24 or approximately 0.042, which is about a 4.2% chance.