A spinner has 8 equally sized sections labeled as A, B, C, D, E, F, G, H. In 160 spins, how many times can you expect to spin on a consonant
There are 5 consonants (B, C, D, F, G) out of a total of 8 letters on the spinner. Therefore, the probability of spinning on a consonant in one spin is 5/8.
Expected number of spins on a consonant in 160 spins:
= (5/8) x 160
= 100
Therefore, you can expect to spin on a consonant 100 times in 160 spins.
A single coin is tossed 300 times. Heads were observed 180 times. What is the long-run relative frequency of tails?
The long-run relative frequency of an event is the ratio of the number of times the event occurs to the total number of trials in the long run.
In this case, the coin is tossed 300 times and heads were observed 180 times. Therefore, the number of times tails were observed is:
300 - 180 = 120
The long-run relative frequency of tails is:
120/300 = 0.4 or 40%
Therefore, the long-run relative frequency of tails is 40%.
To find out how many times you can expect to spin on a consonant in 160 spins, you need to determine the ratio of consonant sections to the total number of sections on the spinner.
Out of the 8 sections labeled A, B, C, D, E, F, G, H, we need to identify the consonant sections. Consonants are all the letters in the alphabet except for vowels (A, E, I, O, U).
In this case, the consonant sections are B, C, D, F, G, and H, which amounts to 6 sections out of a total of 8 sections.
To determine the expected number of spins on a consonant, you would multiply the ratio of consonant sections to the total number of sections by the total number of spins. Using this formula:
Expected number of spins on a consonant = (Number of consonant sections / Total number of sections) * Total number of spins
Expected number of spins on a consonant = (6 / 8) * 160
Expected number of spins on a consonant = (3/4) * 160
Expected number of spins on a consonant = 3 * 20
Expected number of spins on a consonant = 60
Therefore, you can expect to spin on a consonant approximately 60 times out of 160 spins.