You roll two fair dice, a white one and a red one.
a. find P(5 or 6 on the white die and odd number on the red die).
b. Find P(odd number on the white die nad 5 or 6 on the red die).
c. Find P(5 or 6 on the white die nad 5 or 6 on the red die.
Please show work
Thanks
p-1/4=1/6
2#2
To solve these probabilities, we need to consider the numbers on each die independently and then find the probability of the desired outcomes using the principle of multiplication.
a. To find P(5 or 6 on the white die and odd number on the red die), we need to consider the probabilities of rolling 5 or 6 on the white die, and the probability of rolling an odd number on the red die.
The probability of rolling a 5 or 6 on the white die is 2/6 since there are two favorable outcomes (5 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6).
The probability of rolling an odd number on the red die is 3/6 since there are three favorable outcomes (1, 3, and 5) out of six possible outcomes (1, 2, 3, 4, 5, 6).
To find the probability of both events happening, we multiply the two probabilities:
P(5 or 6 on the white die and odd number on the red die) = (2/6) * (3/6) = 6/36 = 1/6.
Therefore, the probability is 1/6.
b. To find P(odd number on the white die and 5 or 6 on the red die), we need to consider the probabilities of rolling an odd number on the white die and rolling 5 or 6 on the red die.
The probability of rolling an odd number on the white die is also 3/6, as there are three favorable outcomes (1, 3, and 5) out of six possible outcomes.
The probability of rolling a 5 or 6 on the red die is 2/6 since there are two favorable outcomes (5 and 6) out of six.
P(odd number on the white die and 5 or 6 on the red die) = (3/6) * (2/6) = 6/36 = 1/6.
Therefore, the probability is 1/6.
c. To find P(5 or 6 on the white die and 5 or 6 on the red die), we need to consider the probability of rolling 5 or 6 on both the white and red dice.
The probability of rolling 5 or 6 on the white die is 2/6.
The probability of rolling 5 or 6 on the red die is also 2/6.
P(5 or 6 on the white die and 5 or 6 on the red die) = (2/6) * (2/6) = 4/36 = 1/9.
Therefore, the probability is 1/9.
a. (1/6+1/6) * (1/6+1/6+1/6) = ?
b. same as a.
c. Use same procedure.
For either-or probabilities, add the individual probabilities. For both/all probabilities, multiply the individual probabilities.