two baseball players bat first and second in the lineup the first batter has on base percentage of 0.46 the second batter has an on base percentage of 0.31 if someone is on base but only 0.23 if the bases are empty at the start of the game what is the probability that both players get on base?
The probability of both/all events occurring is found by multiplying the probabilities of the individual events.
.46 * .31 = ?
To find the probability that both players get on base, we can multiply their individual on-base percentages.
Let's call the first batter A and the second batter B.
Given information:
On-base percentage of Batter A (with someone on base): 0.46
On-base percentage of Batter B (with someone on base): 0.31
On-base percentage of Batter A (with bases empty): 0.23
To find the probability that Batter A gets on base, we use the following formula:
Probability of getting on base for Batter A = On-base percentage of Batter A (with someone on base) + On-base percentage of Batter A (with bases empty) - (On-base percentage of Batter A (with someone on base) multiplied by On-base percentage of Batter A (with bases empty))
Probability of getting on base for Batter A = 0.46 + 0.23 - (0.46 * 0.23)
= 0.69 - 0.1058
= 0.5842
Similarly, for Batter B:
Probability of getting on base for Batter B = On-base percentage of Batter B (with someone on base)
= 0.31
Now, to find the probability that both players get on base, we multiply their individual probabilities:
Probability of both players getting on base = Probability of getting on base for Batter A multiplied by Probability of getting on base for Batter B
Probability of both players getting on base = 0.5842 * 0.31
≈ 0.1806
Therefore, the probability that both players get on base is approximately 0.1806 or 18.06%.
To find the probability that both players get on base, we need to multiply the individual probabilities of each player getting on base.
Let's call the first player "Player A" with an on-base percentage of 0.46 and the second player "Player B" with an on-base percentage of 0.31.
If the bases are empty at the start of the game (which has a 0.23 probability), the probability that Player A gets on base is 0.46. The probability that Player B gets on base, given that Player A is on base, is 0.31.
Therefore, the probability that both players get on base can be calculated as follows:
Probability(Both players get on base) = Probability(Player A gets on base) * Probability(Player B gets on base| Player A already on base)
Probability(Both players get on base) = 0.23 * 0.46 * 0.31
Multiply the three values together to find the answer:
Probability(Both players get on base) = 0.032378
Therefore, the probability that both players get on base is approximately 0.032378 or 3.24%.