Question

The probability of rolling a 6 on a number cube is 1/6. The probability of rolling a 6 twice in a row is (1/6)^2=1/36.

a) The probability of rolling a 6 n times in a row is 1/6 n

b) The probability of rolling a 6 four times in a row is 1/6^4

c) The probability of flipping heads on a coin five times in a row is 1/2^5

d) The probability of rolling a 6 four times in a row is 1/2^4

Answer 1

The probability of rolling a 6 on a number cube is 1/6. The probability of rolling a 6 twice in a row is (1/6)^2 = 1/36. The probability of rolling a 6 n times in a row is 1/6^n.

Step-by-step explanation:

When rolling a 6 on a number cube, the probability is 1/6. When rolling a 6 twice in a row, we multiply the probability of rolling a 6 once by itself: (1/6) * (1/6) = 1/36.

Using this pattern, the probability of rolling a 6 n times in a row is (1/6)^n.

• a) The probability of rolling a 6 n times in a row is 1/6^n.
• b) The probability of rolling a 6 four times in a row is 1/6^4 = 1/1296.
• c) The probability of flipping heads on a coin five times in a row is 1/2^5 = 1/32.
• d) The probability of rolling a 6 four times in a row is incorrect because it should be 1/6^4, not 1/2^4. So, the correct probability is 1/1296.