Solveeit Logo
Login

Question

Question: The probability of four sons to a couple is A. \[\dfrac{1}{4}\] B. \(\dfrac{1}{8}\) C. \(\dfra...

The probability of four sons to a couple is
A. 14\dfrac{1}{4}
B. 18\dfrac{1}{8}
C. 116\dfrac{1}{{16}}
D. None of the above

Explanation

Solution

The female egg contains to two X sex chromosomes whereas male sperm contains one X and one Y sex chromosomes. Male sperm determines the gender of the child.

Complete answer:
Whenever there is a child to a couple, there are two possibilities, either a boy or a girl. Thus, there is a probability of 12\dfrac{1}{2} for a son to be born. The probability for each son is independent of each other. Hence, the probability of four sons to a couple is (12)n{\left( {\dfrac{1}{2}} \right)^n} , where n is the number of sons.
Probability of four sons = (12)4=12×12×12×12=116{\left( {\dfrac{1}{2}} \right)^4} = \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{{16}}

Hence, the correct answer is option (C).

Additional information:
Fertilization in humans takes place when the female egg fused with the male sperm to form a zygote. Half of the genetic material comes from the maternal side and the other half comes from the paternal side. The fusion of two gametes initiates many reactions inside the egg. After fusion, there is a change in the egg membrane, so that the attachment and penetration by more than one spermatozoon cannot occur. In humans, more than one spermatozoon enters an egg, only one spermatozoal nucleus actually merges with the egg nucleus. The most important outcome of fertilization is egg activation, which allows the egg to undergo cell division. The final step is the maturation in which the production of functional eggs develops a reaction that prevents the entry of more than one spermatozoon.

Note: Sexual reproduction is a mode of reproduction in which the young ones are produced through the process of formation & fusion of gametes. Due to the reshuffling of chromosomes and crossing over, sexual reproduction brings about variations so that no two individuals are similar. Genetic changes brought about by sexual reproduction play an important part in the evolution of new forms.