The number cube shown is rolled and the spinner shown is spun. Find P(an odd number and yellow). A six sided number cube and a square spinner divided into four congruent squares are shown. Two of those smaller squares in the spinner are yellow, one is blue, and one is green. The spinner arrow is pointing to the green square.
A. one-fourth
B. three-fourths
C. start fraction 3 over 5 end fraction
D. Start Fraction 3 over 20 End Fraction
The probability of rolling an odd number on the number cube is 3/6 or 1/2 because there are three odd numbers (1, 3, 5) out of six possible outcomes (1, 2, 3, 4, 5, 6).
The probability of landing on the yellow section of the spinner is 2/4 or 1/2 because there are two yellow sections out of four possible outcomes.
Since these two events are independent of each other, we can multiply their probabilities to get the probability of both events happening at the same time.
P(an odd number and yellow) = P(odd number) x P(yellow)
= (1/2) x (1/2)
= 1/4
Therefore, the answer is A. one-fourth.
The number cube shown is rolled and the spinner shown is spun. Find P(5 and blue).A six sided number cube and a square spinner divided into four congruent squares are shown. Two of those smaller squares in the spinner are yellow, one is blue, and one is green. The spinner arrow is pointing to the green square.
The probability of rolling a 5 on the number cube is 1/6 because there is only one 5 out of six possible outcomes.
The probability of landing on the blue section of the spinner is 1/4 because there is only one blue section out of four possible outcomes.
Since these two events are independent of each other, we can multiply their probabilities to get the probability of both events happening at the same time.
P(5 and blue) = P(5) x P(blue)
= (1/6) x (1/4)
= 1/24
Therefore, the answer is 1/24.
There are 9 red gum balls, 5 green gum balls, 8 yellow gum balls, and 8 blue gum balls in a machine. Find P(green, then yellow).
A. start fraction 40 over 900 end fraction
B. The term shows 5 over 30.
C. The term shows 8 over 30.
D. start fraction 40 over 870 end fraction
There are 30 gum balls in the machine in total.
The probability of picking a green gum ball first is 5/30 because there are 5 green gum balls out of 30 in total.
The probability of picking a yellow gum ball second, given that we already picked a green gum ball, is 8/29 because there will be 29 gum balls left in the machine after picking one out, and 8 of them will be yellow.
Since these two events are dependent (the outcome of the first event affects the probability of the second event), we need to multiply their probabilities to get the probability of both events happening in the given order.
P(green, then yellow) = P(green) x P(yellow|green)
= (5/30) x (8/29)
= 40/870
Therefore, the answer is D. start fraction 40 over 870 end fraction.
To find the probability of rolling an odd number and landing on a yellow square, we need to determine both the number of favorable outcomes and the total number of possible outcomes.
Let's start with the number cube. Since it is a standard six-sided cube, the total number of possible outcomes when rolling it is 6.
Out of these 6 outcomes, we are interested in rolling an odd number. The odd numbers on a six-sided cube are 1, 3, and 5. Therefore, the number of favorable outcomes for rolling an odd number is 3.
Moving on to the spinner, we see that it is divided into four congruent squares, two of which are yellow, one is blue, and one is green. The spinner arrow is pointing to the green square. Since we are interested in landing on a yellow square, we have a single favorable outcome.
To find the total number of possible outcomes with the spinner, we count the congruent squares, which is 4 in this case.
Finally, we multiply the number of favorable outcomes for the number cube (3) by the number of favorable outcomes for the spinner (1), and we divide that product by the total number of outcomes for the number cube (6) and spinner (4).
Thus, the probability of rolling an odd number and landing on a yellow square is:
(3 * 1) / (6 * 4) = 3 / 24 = 1 / 8.
The corresponding fraction for this probability is Start Fraction 1 over 8 End Fraction. However, none of the given options match this fraction. As a result, none of the options provided (A, B, C, D) is the correct answer.