1. In a classroom of 20 students, show that there are at least two students with

Question

1. In a classroom of 20 students, show that there are at least two students with the birthdays in the same month.

2. Suppose there is a class and that an assignment is worth 100 points. Possible scores range from 0 to 20.How many students must be in the class in order to guarantee that that at least two students receive the same score on the assignment?

3. Suppose a fair coin is tossed 4 times.

(a.) Write out all possible outcomes (i.e. HHTT, etc).

(b.) What is the probability of obtaining four tails?

(c.) What is the probability of obtaining two heads and two tails?

(d.) What is the probability of no heads?

(e.) What is the probability of obtaining at least 1 head?

Explanation / Answer

1. As , there are only 12 months .
SO , there can br maximum 12 student who have birthday in differnet months,
Rest of 8 will select one month among 12 months per student.

Hence , there are at least two students with the birthdays in the same month.

2. 22 students ( 0 to 20 , thre are 21 scores. So, no. of students must be atleast one more than 21)

3.
TTTT
TTTH
TTHT
TTHH

THTT
THTH
THHT
THHH

HTTT
HTTH
HTHT
HTHH

HHTT
HHTH
HHHT
HHHH

b)P = favourable case / total case
from above we can count ,
P = 1/16

c) P = favourable case / total case
from above we can count ,
P = 6/16 =3/8

d)no heads means four tails,
P = favourable case / total case
from above we can count ,
P = 1/16

e) P (atleast one head) = 1 - P(no head)

P = 1-1/16 = 15/16

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