Question

There are 28 students whose last names begin with the letters G, H, J, or K. Information about the probability of randomly selecting one of these students is listed below • probability of selecting a student whose last name begins with G: 7 • probability of selecting a student whose last name begins with G or H: 5 14 O How many of these students have a last name that begins with H?

A4
B5
C6
D7​

Answer 1

5

We know that there are 28 students in total, so:

G + H + J + K = 28

We also know the following probabilities:

P(G) = 7/28

P(G or H) = 5/14

The probability of selecting a student whose last name begins with G or H can be expressed as:

P(G or H) = P(G) + P(H) - P(G and H)

Since the events "selecting a student whose last name begins with G" and "selecting a student whose last name begins with H" are mutually exclusive (a student cannot have a last name that begins with both G and H), P(G and H) = 0. Therefore, we have:

5/14 = 7/28 + P(H)

Simplifying the equation, we get:

P(H) = 5/14 - 7/28 = 5/28

So the probability of selecting a student whose last name begins with H is 5/28. To find the number of students whose last name begins with H, we can multiply this probability by the total number of students:

H = P(H) x 28 = 5/28 x 28 = 5

Therefore, there are 5 students whose last name begins with H.

*IG: whis.sama_ent*