Question

The following is a table of the heights of​ mother's and their​ daughter's.

			Daughter
		55 to 60	60 to 65	65 to 70	70 to 75	Total
	55 to 60	43	138	13	0	194
Mother	60 to 65	38	648	294	4	984
	65 to 70	2	67	118	8	195
	70 to 75	0	0	1	1	2
	Total	83	853	426	13	1375

          Answer the following based on the table leaving answers to 4 decimal​ places:

1. What is the probability that a daughter is 60 to 65 inches​ tall? nothing

2. What is the probability that a mother will NOT be 55 to 60 inches​ tall? nothing

3. What is the probability that a mother will be 65 to 70 inches tall OR the daughter will be 70 to 75 inches​ tall?  nothing

4. What is the probability that a daughter will be 60 to 65 inches​ tall, GIVEN that the mother is 65 to 70 inches​ tall? nothing

5. Assume that two mothers are selected WITHOUT replacement. What is the probaility that both will be 55 to 60 inches​ tall? nothing

6. Assume that two daughters are selected WITH replacement. What is the probability that they are both 65 to 70 inches​ tall? nothing

Answer 1

1. The probability that a daughter is 60 to 65 inches​ tall

= 853/1375 = 0.62036 = 0.6204

2. The probability that a mother will NOT be 55 to 60 inches​ tall

= 1 - 194/1375 = 0.85890 = 0.8589

3. The probability that a mother will be 65 to 70 inches tall OR the daughter will be 70 to 75 inches​ tall

= 195/1375 + 13/1375 - 8/1375 = 0.14545 = 0.1455

4. The probability that a daughter will be 60 to 65 inches​ tall, GIVEN that the mother is 65 to 70 inches​ tall

= 67/195 = 0.34358 = 0.3436

5. The probaility that both will be 55 to 60 inches​ tall

= (194C2)/(1375C2) = 0.01981 = 0.0198

6. The probability that they are both 65 to 70 inches​ tall

= (426/1375)×(426/1375) = 0.09598 = 0.0960